throughout. It is commonly much colder aloft; ita allo of different conftitutions. Below it is warm, loaded with vapour, and very expanfible; above it is cold, much drier, and less expanfible, both by its drynels and its rarity. The currents of wind are often difpofed in ftrata, which long retain their places; and as they come from diffet regions, are of different temperatures and Eferent conftitutions. We cannot therefore determine the expansion of the whole ftratum with precifion, and must be contented with an approximation. The belt approximation that we can make, is, by fuppofing the whole ftratum of a mean temperature between thofe of its upper and lower extremity, and employing the expantion corresponding to that mean temperature. This, however, is founded on a gratuitous fuppofition, that the whole intermediate ftratum expands alike, and that the expanfion is equable in the different intermediate temperatures; but neither of thefe are warranted by experiment. Rare air-expands lefs than what is denfer; and therefore the general expansion of the whole ftratum renders its density more uniform. Dr Horfley has pointed out fome curious confequences of this in Phil. Tran Vol. LXIV. There is a particular elevation, at which the general expanfion, inftead of dainihing the denfity of the air, increases it by the fuperior expanfion of what is below; and we know that the expanfion is not equable in the intermediate temperatures: but we cannot find out I. Subtract the logarithm of the barometrical a which will give us a more accurate correc-height at the upper ftation from the logarithm of in, than by taking the expanfion for the mean temperature.

this ftate it may contain a confiderable portion of other metals, particularly of filver, bifmuth, and tin, which will diminish its specific gravity. It has been obtained by revivification from cinnabar of the specific gravity 14'229, and it is thought very fine if 1365. Sir George Shuckburgh found the quickfilver which agreed precifely with the atmospherical obfervations on which the rules are founded, to have the specific gravity 1361. It is feldom obtained so heavy. It is evident that these variations will change the whole refults; and that it is abfolutely neceffary, to obtain precision, that we know the density of the mercury employed The fubtangent of the atmospherical logarithmic, or the height of the homogeneous atmosphere, will increase in the fame proportion with the density of the mercury; and the elevation correfponding to one tenth of an inch of barometric height will change in the fame proportion. We must be contented with the remaining imperfections. For any purpose that can be answered by fuch measure. ments of great heights, the method is fufficiently exact; but it is quite inadequate to the purpofe of taking accurate levels, for directing the conftruction of canals, aqueducts, and other works of this kind, where extreme precifion is abfolutely neceffary.

When this is done, we have carried the method of meaturing heights by the barometer as far as it' cago; and this fource of remaining error makes ineedlefs to attend to fome other very minute equations which theory points out. Such is the Ciminution of the weight of the mercury by the change of distance from the centre of the earth. This accompanies the diminution of the weight of the air, but neither fo as to compenfate it, nor to go along with it pari paffu. After all, there are cafes where there is a regular deviation from those rules, of which we cannot give any very fatisfactory account. Thus, in the province of Quito in Peru, which is at a great elevation above the furface of the ocean, the heights obtained by t-fe rules fall confiderably fhort of the real heights; and at Spitfbergen they confiderably ex ced them. It appears that the air in the circumpolar regions, is denier than the air of the temperate climates when of the fame heat, and under the fame preffure; and the contrary feems to be the cake with the air in the torrid zone. It would seem that the specific gravity of air to mercury is at Spitbergen about one to 1c224, and in Peru about 1 to 13100. This difference is with great probability afcribed to the greater drynefs of the

Circumpolar air.

We shall only add a few EASY RULES for the practice of this mode of measurement.

I. M. DE LUC'S METHOD.

that at the lower, and count the index and four firft decimal figures of the remainder as fathoms, the reit as a decimal fraction. Call this the eleva tion.

II. Note the different temperatures of the mercury at the two ftations, and the mean temperature. Multiply the logarithmic expansion corres ponding to this mean temperature (in Table B.) by the difference of the two temperatures, and fubtract the product from the elevation if the barometer has been coldeft at the upper station, otherwife add it. Call the difference or the fum the approximated clevation.

III. Note the difference of the temperatures of the air at the two ftations by a detached thermometer, and alfo the mean temperature and its difference from 32°. Multiply this difference by the expantion of air for the mean temperature, and multiply the approximate elevation by this product, according as the air is above or below 32. The product is the correct elevation in fathoms and decimals.

EXAMPLE. Suppofe that the mercury in the barometer at the lower ftation, was at 294 inches, that its temperature was 50°, and the temperature of the air was 45; and let the height of the mercury at the upper ftation be 25°19 inches, its tem perature 46, and the temperature of the air 39.

Thus we have

This fource of error will always remain; and it al Hts. Temp. is combined with another, which fhould be attended to by all who practife this method of meafuring heights, namely, a difference in the fpecific gravity of the quick-filver. It is thought fufficiently pure for a barometer when it is cleared of all calcinable matter, fo as not to fully the tube. In

I. Log. of 29'4
Log. of 25*19

Elevation in fathoms

B 2

671,191 II. Expanf

Pic de los Reyes)

Fic du Medi

Pic d'Ofano

Lake of Genera

Mount Etna

Must Veluvius

Pyrennees

Mount Hecia in Iceland
Snowdown
Benmore

Ben Lawers

Ben-Glue

Schehallion

Ben Lomond
Tinto

Table Hill, Cape of Good Hope
Gondar city in Abyffinia

7620 to the common barometer for measurement of 9300 heights, on account of their bulk and cumber11700 fomenefs: nay, they are inferior for all philofo8544 phical purpofes in point of accuracy. Their scale 1232 must be determined in all its parts by the com10954 mon barometer; and therefore notwithstanding 3938 their great range, they are susceptible of no great4887 er accuracy, than that with which the scale of a 3555 common barometer can be observed and measu3723 red. This is evident from confidering how the 3858 points of their scale must be afcertained. The 3472 moft accurate method for graduating such a ba3461 rometer would be to make a mixture of vitriolic 3180 acid and water, which should have one 10th of 2342 the density of mercury. Then, let a long tube 3454 ftand verticle in this fluid, and connect its upper 8440 end with the open end of the barometer by a pipe 8082 which has a branch to which we can apply the 14026 mouth. Then if we fuck through this pipe, the 19595 fluid will rife both in the barometer and in the 19391 other tube; and 10 inches rife in this tube will 19290 correfpond to one inch defcent in the common 15670 barometer. In this manner may every point of 9977 the scale be adjusted in due proportion to the 306 reft. But it ftill remains to determine what partiThis laft is fo fingular, that it is neceffary to cular point of the scale correfponds to fome degive the authority on which this determination is termined inch of the common barometer. This founded. It is deduced from nine years obferva- can only be done by an actual comparison; and ties with the barometer at Aftracan by Mr Lecre, this being done, the whole becomes equally accompared with a feries of obfervations made with curate, Except therefore for the mere purpose the fame barometer at St Petersburgh. of chamber amusement, in which cafe the barometer laft described has a decided preference, the common barometer is to be preferred; and our attention fhould be entirely directed to its improvement and portability.

Source of the Nile

Fit of Teneriffe

Chimborazo

Cayambourow

Antifaca

Pichincha
City of Quito

Cafpian Sea below the ocean

This ufe of the barometer has rendered it a very tering intrument to the philofopher and to the traveller; and many attempts have been made of late to improve it, and render it more portable. The improvements have either been directed to the enlargement of its range, or to the more acCrate measurement of its prefent fcale. Of the firft kind are Hooke's wheel barometer, the diaDal barometer, and the horizontal barometer. See BAROMETER, $ 4,6; alfo § 10, 20; for two very ingenious contrivances of Mr Rownings, which are not portable. Of all the barometers with an enlarged fcale the beft is that invented by Dr Hooxe in 1668, and defcribed in the Phil. Tran N° 185. The invention was alfo claimed Huygens and De la Hire; but Hooke's was Fblihed long before.

It confifts of a compound tube ABCDEFG (fig. 51. Pl. 281.) of which the parts AB and DE are equally wide, and EFG as much narrower as we would amplify the fcale. The parts AB and EG falfo be as perfectly cylindrical as poffible. The part HBCDI is filled with mercury, having a vacuum above in AB. IF is filled with a light fid, and FG with another light fluid which will not mix with that in IF. The ciftern G is of the fame diameter as AB. The range of the feparating furface at F is as much greater than that of the furface I, as the area of 1 is greater than that of F. And this ratio is in our choice. This barometer is fre from all the bad qualities of thofe formerly defcnbed, being moft delicately moveable; and is by far the fitteft for a chamber, or amufement, by obfervations on the changes of the atmospheric preffure. The flighteft breeze caufes it to rife and fall, and it is continually in motion.

Bat this, and all other barometers are inferior

For this purpofe it fhould be furnished with two microscopes or magnifying glaffes, one ftationed at the beginning of the fcale; which should either be moveable, fo that it may always be brought to the furface of the mercury in the ciftern, or the ciftern fhould be fo contrived that its furface may always be brought to the beginning of the fcale. The glafs will enable us to fee the coincidence with accuracy. The other microfcope must be moveable, fo as to be fet oppofite to the furface of the mercury in the tube; and the fcale fhould be furnished with a vernier which divides an inch into 1000 parts, and be made of materials of which we know the expansion with great precifion.

For an account of many ingenious contrivances to make the inftrument accurate, portable, and commodious, confult Magellan, Differ. de diverses Inftr. de Phys; Phil. Tranf. Ixvii. ixviii.; Journ. de Phys. xix. 108. 346. xvi. 392. xviii. 391. xxi. 436. xxii. 390.; Sulzer, Act Helvet. iii. 259.; De Luc, Recherches fur les Modifications de l'Atmosphere, i. 401. ii. 459, 490. De Luc's feems the most fimple and perfect of them all. Cardinal de Luynes (Mem. Par. 1768); Prin. De Luc, Recherches, § 63.; Van Swinden's Pofitiones Phyfica; Com. Acad. Petrop. i.; Com. Acad. Petrop. Nov. 100. viii.

SECT. VIII. Of AIR in MOTION.

THUS We have given an elementary account of the diftinguishing properties of air as a heavy and compreffible fluid, and of the general phenomena which are immediate confequences of these pro

perties;

perties; in a fet of propofitions analagous to those which form the doctrines of HYDROSTATICS. We fhall now confider it as moveable and inert. The phenomena confequent on these properties are exhibited in the velocities which air acquires by preffure, in the refiftance which bodies meet with totheir motion thro' the air, and in the impreffion which air in motion gives to bodies exposed to its action. We fhall firft confider the motions of which air is fufceptible when the equilibrium of preffure (whether arifing from its weight or its elafticity) is removed; and next, we shall confider its action on folid bodies expofed to its current, and the refiftance which it makes to their motion through it. In this confideration we shall adapt our invef-1332 feet per fecond. This therefore is the tigation to the circumftances in which compref- velocity with which common air will rush into a fible fluids are moft commonly found. We fhall void; and this may be taken as a standard numconfider air therefore as it is commonly found in ber in pneumatics, as 16 and 32 are ftandard numacceffible fituations, as acted on by equal and pa- bers in the general science of mechanics, expreffing rallel gravity; and we fhall confider it in the fame the action of gravity at the furface of the earth. order in which water is treated in a system of

AIR is about 840 times lighter than water, and the preffure of the atmosphere, fupports water at the height of 33 feet nearly. The height therefore of a homogeneous atmosphere is nearly 33 X 840, or 27720 feet. As for the velocity acquired by any fall, a heavy body by falling one foot acquires the velocity of 8 feet per fecond; and the velocities acquired by falling thro' different heights are as the fquare roots of the heights. Therefore, to find the velocity correfponding to any height, expreffed in feet per fecond, multiply the fquare root of the height by 8. We have therefore in the prefent inftance V=8√2 27220, 8X166,493

HYDRAULICS.

In that science the leading problem is to determine with what velocity the water will move through a given orifice when impelled by fome known preffure; and it has been found, that the beft form in which this moft difficult and intricate propofition can be put, is to determine the velocity of water flowing through this orifice when impelled by its weight alone. Having determined this, we can reduce to this cafe every queftion which can be propofed; for, in place of the preffure of any piston or other mover, we can always fubftitute a perpendicular column of water or air, whose weight shall be equal to the given prefiure. The first problem, therefore, is to determine with what velocity air will rush into a void when im pelled by its weight alone. This is evidently analogous to the hydraulic problem of water flowing

out of a velfel.

And here we must refer our readers to the folutions which have been given of that problem,

under HYDROSTATICS, Part I. and the demonflration that it flows with the velocity which a heavy body would acquire by failing from a height equal to the depth of the hole under the furface of the water in the veffel. In whatever way we attempt to demonstrate that propofition, every step, nay, to the air, or to any fluid whatever. Or, if our every word, of the demonstration applies equally logy of the cafes, we only defire them to recollect an undoubted maxim in regard to motion, that when the moving force and the matter to be moved vary in the fame proportion, the velocity will be the fame. If therefore there be fimilar veffels of air, water, oil, or any other fluid, all of the height of a homogeneous atmosphere, they will all run through equal and fimilar holes with the fame velocity; for in whatever proportion the quantity of matter moving thro' the hole be varied by a variation of denfity, the preffure which forces it out, by acting in circumstances perfectly fimilar, varies in the fame proportion by the fame variation of denfity. We must therefore affume it as the leading propofition, that air rushes from the atmosphere into a void with the velocity which a heavy body would acquire by falling from the top of a homogeneous atmosphere.

readers fhould wish to fee the connection or ana

Greater precifion is not neceffary in this matter. The height of a homogeneous atmosphere is a variable thing, depending on the temperature of the air. If this feems any objection against the ufe of the number 1332, we may retain 8/H in place of it, where H expreffes the height of a homogeneous atmosphere of the given temperature. A variation of the barometer makes no change in the velocity, nor in the height of the homogeneous atmosphere, because it is accompanied by a proportional variation in the density of the air. When it is increased one 10th, for inftance, the denfity force and the matter to be moved are changed in is also increased one roth; and thus the expelling the fame proportion, and the velocity remains the fame. We do not here confider the velocity which the air acquires after its iffuing into the void by its continual expanfion. This may be ascertained by the 39th prop. of Newton's Principia, i. Nay, which appears very paradoxical, if a cylinder of be compreffed by a pifton loaded with a weight, air, communicating in this manner with a void, which preffes it down as the air flows out, and efflux with ftill be the fame, however great the prefthus keeps it of the fame density, the velocity of fure may be: for the first and immediate effect of the load on the pifton is to reduce the air in the cylinder to fuch a denfity that its elafticity fhall of the air will be increased in the fame proportion exactly balance the load; and because the elafticity of air is proportional to its denfity, the denfity with the load, that is, with the expelling power; for we are neglecting at prefent the weight of the fible effect. Therefore, fince the matter to be included air as too inconfiderable to have any fenmoved is increafed in the fame proportion with the preffure, the velocity will be the fame as before.

It is equally eafy to determine the velocity with which the air of the atmosphere will rush into a pace containing rarer air. Whatever may be the denfity of this air, its elafticity, which follows the proportion of its denfity, will balance a proporit is the exccfs of this laft only which is the motional part of the preffure of the atmosphere; and ving force. The matter to be moved is the fame as before. Let D be the natural density of the air, into which it is fuppofed to run, and let P be the and the density of the air contained in the vessel

preffure